Simplify Square Root of 33686

What is the square root of 33686 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√33686 = A√B

Unfortunately, the square root of 33686 cannot be simplified. Thus, here is the answer to the square root of 33686 in its simplest form:

√ 33686 = √ 33686

Here are two different methods we used to determine why the square root of 33686 cannot be simplified.

1) To be able to simplify the square root of 33686, one of the factors of 33686 other than 1 must be a perfect square. The factors of 33686 are 1, 2, 16843, and 33686. Since none of these factors are perfect squares, the square root of 33686 cannot be simplified.

2) To be able to simplify the square root of 33686, all the prime factors of 33686 cannot be unique. When we did prime factorization of 33686, we found that 2 x 16843 equals 33686. Since all the prime factors are unique, the square root of 33686 cannot be simplified.

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